The $k$-Cap Process on Geometric Random Graphs
Probability
2022-11-16 v2 Discrete Mathematics
Abstract
The -cap (or -winners-take-all) process on a graph works as follows: in each iteration, exactly vertices of the graph are in the cap (i.e., winners); the next round winners are the vertices that have the highest total degree to the current winners, with ties broken randomly. This natural process is a simple model of firing activity in the brain. We study its convergence on geometric random graphs, revealing rather surprising behavior.
Keywords
Cite
@article{arxiv.2203.12680,
title = {The $k$-Cap Process on Geometric Random Graphs},
author = {Mirabel Reid and Santosh S. Vempala},
journal= {arXiv preprint arXiv:2203.12680},
year = {2022}
}
Comments
We edited to extend the analysis of the discrete k-cap process from 1-D interval graphs to constant d-dimensional graphs